Finite capacity production planning with random demand and limited information

Albritton, Michael

Shapiro, Alexander

Spearman, Mark

Production planning has a fundamental role in any manufacturing operation. The problem is to decide what type of, and how much, product should be produced in future time periods. The decisions should be based on many factors, including period machine capacity, profit margins, holding costs, etc. Of primary importance is the estimate of demand for manufacturer's products in upcoming periods. Our focus is to address the production planning problem by including in our models the randomness that exists in our estimates for future demands. We solve the problem with two variants of Monte Carlo sampling based optimization techniques, to which we refer as "simulation based optimization" methods. The first variant assumes that we know the actual demand distribution (assumed to be continuous) with which we approximate the true optimal solution by averaging sample estimates of the corresponding expected value function. The second approach is useful when we have limited information about the demand distribution. We illustrate the robustness of the approach by comparing a three mass-point approximation of the continuous distribution to the results obtained using the continuous distribution. This second approach is particularly appealing as it results in a solution that is close to optimal while being much faster than the continuous distribution approach.